Field of the Invention
The present invention relates to an electron microscope and also to a method of measuring aberrations.
Description of Related Art
A scanning transmission electron microscope (STEM) is an electron microscope for obtaining scanning transmission electron microscope (STEM) images by scanning a focused electron beam over a sample, detecting a signal arising either from electrons transmitted through the sample or from scattering electrons, and mapping the intensities of the signal in synchronism with the scanning. In recent years, scanning transmission electron microscopes have attracted attention as electron microscopes capable of providing quite high spatial resolutions at the atomic level.
A segmented detector whose detection surface is divided into plural detector segments is known as an electron detector equipped in such a scanning transmission electron microscope. The segmented detector has independent detection systems for the detector segments, respectively. Each detection system detects only electrons striking a respective one of the detector segments on the detection surface. A scanning transmission electron microscope performs imaging while bringing the detection surface into coincidence with the diffraction plane. That is, this is equivalent to detecting electrons transmitted and scattering within a certain solid-angle region from a sample. Consequently, this presents the advantage that the use of a segmented detector permits one to simultaneously measure the solid angle dependence of scattering of electrons caused by the sample and to obtain a quantitative evaluation (see, for example, JP-A-2011-243516).
JP-A-2012-22971 discloses a method of measuring aberrations in a scanning transmission electron microscope equipped with such a segmented detector. In this known method, bright field images are obtained from detector segments, respectively, which are different in position, by the use of the segmented detector. At the same time, dark field images are derived. Aberration coefficients are computed using these simultaneously obtained final images to be observed. In this method of measuring aberrations, a dark field image undergoing a relatively small deviation is used as a position reference and so the accuracy at which the aberration coefficients are calculated can be improved. Aberration correction is made based on the results. Consequently, higher resolution can be accomplished.
The principle of measuring aberrations in a scanning transmission electron microscope is now described. FIG. 9A is a schematic ray diagram of one example of orbit of an electron beam EB from a vicinity of a sample S to a detector 120 (having a detection surface 123) in obtaining a bright field image in the scanning transmission electron microscope.
The sample S is placed at a position remote from the front focal plane 113a of an objective lens 113 by the focal distance. The detector 120 is installed at a position located at a distance equal to the camera length from the sample S. FIG. 9A shows the manner in which the electron beam EB passes through the front focal plane 113a of the objective lens 113 and is converged toward the sample S by the converging action of the objective lens 113.
The angle of convergence α is the angle of incidence of the electron beam EB to the sample S and the azimuthal angle θ is the azimuthal angle of the beam EB on the sample S (see FIG. 9B). Where there is no aberration, the beam EB is focused into one point on the sample S as indicated by the broken line irrespective of the angle of convergence α and the azimuthal angle θ. On the other hand, where there is aberration (geometric aberration), as the angle of convergence α to the sample S increases, the electron beam EB intersects the optical axis 2 more forwardly of the sample S. As the angle of convergence α of the beam increases, the position of incidence of the beam on the sample deviates more from the intended position of incidence of the beam. If this aberration is attributed to the spherical aberration in the objective lens 113, the deviation is proportional to the cube of the angle of convergence α as is well known in the art.
Under such influence of aberration, if an electron beam EB1 that has passed over the optical axis 2 forms a bright field image as shown in FIG. 10A, a bright field image formed by an electron beam EB2 having an angle of convergence α (α≠0) to the sample S involves a positional deviation relative to the bright field image of FIG. 10A as shown in FIG. 10B, because the beam EB2 needs to be shifted further in order to image an atom A (in other words, to irradiate the atom A) due to a deviation of the incident position on the sample caused by the aberration.
That is, plural bright field images formed by electron beams having different angles of convergence α inevitably involve their mutual positional deviations due to aberrations. More specifically, it is assumed that one final image of the sample S is taken as a reference and that the amount of positional deviation of each bright field image of the sample is represented by a positional deviation vector Fα,θ. An oppositely directed vector corresponds to a geometric aberration vector Gα,θ indicating an aberration appearing in each bright field image.
On the other hand, the front focal plane (also referred to as the aperture plane) 113a of the objective lens 113 is an angular spatial plane of the electron beam EB. That is, as conceptually illustrated in FIG. 9B, if each position of the electron beam in the front focal plane 113a is represented in terms of polar coordinates, the radial component and the angular component of the position can be represented uniquely by the angle of convergence α and the azimuthal angle θ, respectively. An aberration function χ at the front focal plane 113a is represented as the sum of the following wave aberrations which are a function of these angle of convergence α and azimuthal angle θ. In high-resolution imaging at the atomic level, if the fact that only on-axis aberrations are treated is taken into account, the aberration function χ (α, θ) is given by
      χ    ⁡          (              α        ,        θ            )        =            focal      ⁢                          ⁢      deviation      ⁢                          ⁢              (        defocus        )              +          two      ⁢              -            ⁢      fold      ⁢                          ⁢      astigmatism        +          on      ⁢              -            ⁢      axis      ⁢                          ⁢      coma        +          three      ⁢              -            ⁢      fold      ⁢                                        ⁢                                      ⁢      astigmatism        +          spherical      ⁢                          ⁢      aberration        +          star      ⁢                          ⁢      aberration        +          four      ⁢              -            ⁢      fold      ⁢                          ⁢      astigmatism        +          fourth      ⁢              -            ⁢      order      ⁢                          ⁢      coma        +          three      ⁢              -            ⁢      lobe      ⁢                          ⁢      aberration        +          five      ⁢              -            ⁢      fold      ⁢                          ⁢      astigmatism        +          fifth      ⁢              -            ⁢      order      ⁢                          ⁢      spherical      ⁢                          ⁢      aberration        +          six      ⁢              -            ⁢      fold      ⁢                                        ⁢                                      ⁢      astigmatism      
That is, the aberration function χ (α, θ) is given by the following Eq. (A):
                              χ          ⁡                      (                          α              ,              θ                        )                          =                                            1              2                        ⁢                          α              2                        ⁢                          o              2                                +                                    1              2                        ⁢                          α              2                        ⁢                          a              2                        ⁢                                                  ⁢                          cos              ⁡                              (                                  2                  ⁢                                      (                                          θ                      -                                              θ                                                  a                          ⁢                                                                                                          ⁢                          2                                                                                      )                                                  )                                              +                                    1              2                        ⁢                          α              3                        ⁢                          p              3                        ⁢                                                  ⁢                          cos              ⁡                              (                                  θ                  -                                      θ                                          p                      ⁢                                                                                          ⁢                      3                                                                      )                                              +                                    1              3                        ⁢                          α              3                        ⁢                          a              3                        ⁢                                                  ⁢                          cos              ⁡                              (                                  3                  ⁢                                      (                                          θ                      -                                              θ                        a3                                                              )                                                  )                                              +                                    1              4                        ⁢                          α              4                        ⁢                          o              4                                +                                    1              4                        ⁢                          α              4                        ⁢                          q              4                        ⁢                                                  ⁢                          cos              ⁡                              (                                  2                  ⁢                                      (                                          θ                      -                                              θ                                                  q                          ⁢                                                                                                          ⁢                          4                                                                                      )                                                  )                                              +                                    1              4                        ⁢                          α              4                        ⁢                          a              4                        ⁢                                                  ⁢                          cos              ⁡                              (                                  4                  ⁢                                      (                                          θ                      -                                              θ                                                  a                          ⁢                                                                                                          ⁢                          4                                                                                      )                                                  )                                              +                                    1              5                        ⁢                          α              5                        ⁢                          p              5                        ⁢                                                  ⁢                          cos              ⁡                              (                                  θ                  -                                      θ                                          p                      ⁢                                                                                          ⁢                      5                                                                      )                                              +                                    1              5                        ⁢                          α              5                        ⁢                          r              5                        ⁢                                                  ⁢                          cos              ⁡                              (                                  3                  ⁢                                      (                                          θ                      -                                              θ                                                  r                          ⁢                                                                                                          ⁢                          5                                                                                      )                                                  )                                              +                                    1              5                        ⁢                          α              5                        ⁢                          a              5                        ⁢                                                  ⁢                          cos              ⁡                              (                                  5                  ⁢                                      (                                          θ                      -                                              θ                                                  a                          ⁢                                                                                                          ⁢                          5                                                                                      )                                                  )                                              +                                    1              6                        ⁢                          α              6                        ⁢                          o              6                                +                                    1              6                        ⁢                          α              6                        ⁢                          a              6                        ⁢                                                  ⁢                          cos              ⁡                              (                                  6                  ⁢                                      (                                          θ                      -                                              θ                                                  a                          ⁢                                                                                                          ⁢                          6                                                                                      )                                                  )                                              +                                    (        A        )            
The components Gα and Gθ of the geometric aberration vector Gα,θ in the direction of the angle of convergence and in the direction of the azimuthal angle, respectively, are obtained by taking the partial differentials of the aberration function χ with respect to the angle of convergence α and the azimuthal angle θ.
                              G                      α            ,            θ                          =                              (                                          G                a                            ,                              G                θ                                      )                    =                      (                                                            λ                                      2                    ⁢                                                                                  ⁢                    π                                                  ⁢                                                      ∂                    χ                                                        ∂                    α                                                              ,                                                λ                                      2                    ⁢                                                                                  ⁢                    π                                                  ⁢                                  1                  α                                ⁢                                                      ∂                    χ                                                        ∂                    θ                                                                        )                                              (        B        )            
That is, a bright field image is obtained for each of plural combinations of values of the angle of convergence α and the azimuthal angle θ. This gives rise to as many geometric aberration vectors Gα,θ as the number of these combinations. Then, aberration coefficients can be calculated by mathematically processing (e.g., applying a least squares method to) these vectors.
With respect to the angle of convergence α and the azimuthal angle θ of the electron beam, the position of the beam on the detection surface, for example, should be identified. For example, a multi-segmented detector is prepared which has multiple detector segments providing different detection positions with which the convergence angle α and the azimuthal angle θ are associated. Bright field images are obtained simultaneously from an electron beam incident on the individual detector segments of the detector together with positional information about the detection surface (i.e., angular information (convergence angle α and azimuthal angle θ) about the electron beam EB incident on the detector segments). Plural geometric aberration vectors Gα,θ are computed for these bright field images. Since each aberration is a function having convergence angle α and azimuthal angle θ (radial component and angular component at the front focal plane) as variables, it is necessary to divide the detector segments at least into two groups for both variables.
As the number of geometric aberration vectors Gα,θ needed to calculate each aberration coefficient is increased (i.e., as the number of detector segments is increased), aberrations of low orders can be computed at higher accuracy.
FIG. 11 schematically illustrates a method of measuring aberrations in a scanning transmission electron microscope equipped with a segmented detector. As shown, an electron beam EB is focused onto a sample S. If aberrations are present in the illumination system, the incident position on the sample S varies for each different convergence angle and so the beam is not focused into one point.
FIG. 12A is a bright-field STEM image obtained from a detector segment D1. FIG. 12B is a bright-field STEM image obtained from a detector segment D2. FIG. 12C is a bright-field STEM image obtained from a detector segment D3.
If bright-field STEM images are captured by a segmented detector having the plural detector segments D1, D2, and D3, the angle of incidence of the detected electron beam EB differs among the different detector segments D1, D2, and D3. Therefore, the incident position of the electron beam EB on the sample S deviates according to the amount of deviation in the illumination system as shown in FIG. 11. As a result, the whole bright-field STEM image shifts as shown in FIGS. 12A-12C. Aberration coefficients can be computed from this image shift.
FIG. 13 is a schematic plan view of one example of the segmented detector 120. In this detector 120, each of detector segments D1-D4 has a sectorial shape, for example, as shown. If aberrations are measured in these detector segments D1-D4, the resulting images are blurred because these segments D-D4 are spread greatly (i.e., the angle of incidence is spread greatly). This makes it difficult to compute the amount of movement of each image accurately. Especially, the sectorial detector segments are spread much circumferentially and, therefore, if there are high-order aberrations of angular symmetry, the images are blurred conspicuously.